Question

A circle has a chord that goes from `pi/3` to `pi/4` radians on the circle. If the area of the circle is `49 pi`, what is the length of the chord?

Answer 1

The length of the chord is `=1.83u`

Explanation:

The angle subtended at the center of the circle is

`hat(AOB)=theta=pi/3-pi/4=pi/12`

The area of the circle is

`A=pir^2=49pi`

Therefore,

The radius of the circle is

`r=sqrt49=7`

The length of the chord is

`AB=2*AC=2*AOsin(theta/2)`

`=2*7*sin(pi/24)`

`=14*0.13`

`=1.83u`